The current Dalai Lama is not the only one to bear this name: it has been borne by all Dalai Lamas except the very first one (1391–1474), whose monastic name was Ge(n)dun Drub or Drup(a).Also see: https://en.wikipedia.org/wiki/List_of_Dalai_Lamas (in English).
Gyatso is the name of a character in Avatar: the Last Airbender on Nickelodeon. He was Aang's friend and mentor prior to the begin of the series and is seen in a few later episodes as part of a flashback.
Also see: https://en.wikipedia.org/wiki/List_of_Dalai_Lamas (in English).